Enumerating the operators of an effective field theory

TL;DR

This paper presents an alternative method to count high-dimensional operators in the SMEFT, confirming previous results and providing additional insights, with a versatile approach applicable to other models and implemented in software.

Contribution

It introduces a new method for enumerating SMEFT operators that cross-checks existing counts and offers extra information, applicable to various models.

Findings

Confirmed the number of SMEFT operators up to dimension 15

Provided additional details about the operators beyond counting

Developed a computer code for the enumeration process

Abstract

Until recently little was known about the high-dimensional operators of the standard model effective field theory (SMEFT). However, in the past few years the number of these operators has been counted up to mass dimension 15 using techniques involving the Hilbert series. In this work I will show how to perform the same counting with a different method. This alternative approach makes it possible to cross-check results (it confirms the SMEFT numbers), but it also provides some more information on the operators beyond just counting their number. The considerations made here apply equally well to any other model besides SMEFT and, with this purpose in mind, they were implemented in a computer code.